Mathematician:Felix Christian Klein

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German mathematician best known for his work establishing the connections between geometry and group theory.

Architect of the Erlangen program, which classifies geometries according to their symmetry groups.

Noted for the Klein bottle and the Klein $4$-group.

Not to be confused with Morris Kline.




  • Born: 25 April 1849 in Düsseldorf, Prussia (now Germany)
  • 1875: Married Anne Hegel, the granddaughter of the philosopher Georg Wilhelm Friedrich Hegel
  • Died: 22 June 1925 in Göttingen, Germany

Theorems and Definitions

Results named for Felix Christian Klein can be found here.

Definitions of concepts named for Felix Christian Klein can be found here.


  • 1868: Über die Transformation der allgemeinen Gleichung des zweiten Grades zwischen Linien-Koordinaten auf eine kanonische Form
  • 1882: Ueber Riemann's Theorie der Algebraischen Functionen und ihre Integrale
  • 1884: Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom 5ten Grade (English translation by G.G. Morrice: Lectures on the Icosahedron; and the Solution of Equations of the Fifth Degree, 1914)
  • 1890, 1892: Vorlesungen über die Theorie der elliptischen Modulfunktionen (2 volumes) (with Robert Fricke (2 volumes: 1890 and 1892)
  • 1893: Evanston Colloquium (before the Congress of Mathematics, reported and published by Alexander Ziwet, 1894)
  • 1894: Über die hypergeometrische Funktion
  • 1894: Über lineare Differentialgleichungen der 2. Ordnung
  • 1895: Vorträge über ausgewählte Fragen der Elementargeometrie) (English translation by W.W. Beman and D.E. Smith: Famous Problems of Elementary Geometry, 1897)
  • 1897 - 1910: Theorie des Kreisels (with Arnold Sommerfeld)
  • 1897 - 1912: Vorlesungen über die Theorie der automorphen Funktionen (2 volumes: the second volume was published in three parts) (with Robert Fricke)
  • 1897: Mathematical Theory of the Top (Princeton address, New York)
  • 1908: Elementarmathematik vom höheren Standpunkte aus
  • 1925: Elementarmathematik vom höheren Standpunkte aus (3rd edition)
  • 1939: Elementary Mathematics from an Advanced Standpoint: Geometry, Volume 2 (translated by Earle Raymond Hedrick and Charles Albert Noble from Elementarmathematik vom höheren Standpunkte aus, 3rd edition)

Notable Quotes

Plato said, "God is a geometer." Jacobi changed this to, "God is an arithmetician." Then came Kronecker and fashioned the memorable expression, "God created the natural numbers, and all the rest is the work of man."
-- Quoted as an epigraph to the preface to 1980: David M. Burton: Elementary Number Theory (revised ed.)

Also known as

Felix Christian Klein is also sometimes reported as Christian Felix Klein.


... and while we're about it

A mathematician named Klein
Thought the Möbius band was divine.
He said, "If you glue
The edges of two,
You get a weird bottle like mine."

(Quoted by Martin Gardner in one of his Mathematical Games columns in Scientific American, c. $1960$ – $70$)